两类风险模型破产概率上界数值解法的研究

发布时间：2018-02-25 01:19

本文关键词： 风险模型破产概率相依系数利率因素干扰系数相依风险模型　出处：《延安大学》2013年硕士论文　论文类型：学位论文

【摘要】：研究了两类风险模型破产概率上界数值解方法.给定各随机过程及随机变量的具体分布；并考虑模型中两类索赔发生相依和不相依时，，给出了破产概率、生存概率等精算指标的数值模拟分析；同时讨论了干扰系数、利率因素、相依系数等对破产概率上界的影响.全文的结构和内容安排如下：首先,概括性介绍了风险理论的发展史,风险理论的研究成果和主要研究目的及意义,重点介绍了风险模型破产理论的有关知识. 其次,简单的介绍了该论文中用到的一些基本概念、基本公式、随机过程、研究计算方法及几个命题证明. 再次,利用MATLAB软件,对两类模型的破产概率上界等一些常见精算指标的进行数值模拟.引入了索赔过程具有相依性和带利率的双险种风险模型，对第一类模型讨论了相依系数对破产概率的影响程度；对第二类模型给出此模型在保单到达的总份数和理赔发生的总次数分别服从参数不同的Poisson过程时调节系数满足的方程及数值计算方法；并结合实例进行数值模拟,同时也研究了利率因素对破产概率的影响. 最后,对该论文进行概括性的总结,同时指出在本论文的基础上,我们将要开展的工作.
[Abstract]:In this paper, the upper bound numerical solution method of ruin probability for two kinds of risk models is studied. Given the specific distribution of each stochastic process and random variable, the ruin probability is given when the two kinds of claims are dependent or not dependent in the model. At the same time, the influence of interference coefficient, interest rate factor and dependency coefficient on the upper bound of ruin probability is discussed. The structure and content of this paper are as follows:. First of all, the history of risk theory, the research results of risk theory, the main purpose and significance of risk theory are introduced, and the knowledge of risk model bankruptcy theory is introduced in detail. Secondly, some basic concepts, basic formulas, stochastic processes, research methods and propositional proofs used in this paper are briefly introduced. Thirdly, by using MATLAB software, some common actuarial indexes, such as the upper bound of ruin probability of the two kinds of models, are numerically simulated, and a double-type risk model with interest rate and dependent claim process is introduced. For the first model, the influence of dependency coefficient on ruin probability is discussed. For the second kind of model, the equation and the numerical calculation method of the adjustment coefficient are given when the total number of policies arrived and the total number of claims taken from the Poisson process with different parameters, and the numerical simulation is carried out with an example. At the same time, the influence of interest rate on ruin probability is also studied. Finally, the paper is summarized, and the work we will carry out is pointed out on the basis of this paper.
【学位授予单位】：延安大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224;O211.67

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